Bayesian Inference for Repeated Measures Under Informative Sampling

Abstract

Survey data are often randomly drawn from an underlying population of inferential interest under a multistage, complex sampling design. A sampling weight proportional to the number of individuals in the population that each sampled individual represents is released. The sampling design is informative with respect to a response variable of interest if the variable correlates with the sampling weights. The distribution for the variables of interest differs in the sample and in the population, requiring correction to the sample distribution to approximate the population. We focus on model-based Bayesian inference for repeated (continuous) measures associated with each sampled individual. We devise a model for the joint estimation of response variable(s) of interest and sampling weights to account for the informative sampling design in a formulation that captures the association of the measures taken on the same individual incorporating individual-specific random-effects. We show that our approach yields correct population inference on the observed sample of units and compare its performance with competing method via simulation. Methods are compared using bias, mean square error, coverage, and length of credible intervals. We demonstrate our approach using a National Health and Nutrition Examination Survey dietary dataset modeling daily protein consumption.